Solve for $x$ and $y$ by deriving an expression for $y$ from the second equation, and substituting it back into the first equation. $\begin{align*}-6x+6y &= -6 \\ -2x-7y &= -3\end{align*}$
Begin by moving the $x$ -term in the second equation to the right side of the equation. $-7y = 2x-3$ Divide both sides by $-7$ to isolate $y$ $y = {-\dfrac{2}{7}x + \dfrac{3}{7}}$ Substitute this expression for $y$ in the first equation. $-6x+6({-\dfrac{2}{7}x + \dfrac{3}{7}}) = -6$ $-6x - \dfrac{12}{7}x + \dfrac{18}{7} = -6$ Simplify by combining terms, then solve for $x$ $-\dfrac{54}{7}x + \dfrac{18}{7} = -6$ $-\dfrac{54}{7}x = -\dfrac{60}{7}$ $x = \dfrac{10}{9}$ Substitute $\dfrac{10}{9}$ for $x$ back into the top equation. $-6( \dfrac{10}{9})+6y = -6$ $-\dfrac{20}{3}+6y = -6$ $6y = \dfrac{2}{3}$ $y = \dfrac{1}{9}$ The solution is $\enspace x = \dfrac{10}{9}, \enspace y = \dfrac{1}{9}$.